Fourier transform of Lp on real rank 1 semisimple Lie groups

Takeshi KAWAZOE

doi:10.2969/jmsj/03440561

Fourier transform of L^p on real rank 1 semisimple Lie groups

Takeshi KAWAZOE

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JOURNAL FREE ACCESS

1982 Volume 34 Issue 4 Pages 561-579

DOI https://doi.org/10.2969/jmsj/03440561

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Published: 1982 Received: March 09, 1981 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) Harish-Chandra, Harmonic analysis on real reductive groups I, J. Functional Analysis, 19 (1975), 104-204.
2) Harish-Chandra, Harmonic analysis on real reductive groups II, Invent. Math., 36 (1976), 1-55.
3) Harish-Chandra, Harmonic analysis on real reductive groups III, Ann. of Math., 104 (1976), 117-201.
4) K. D. Johnson, Paley-Wiener theorems on groups of split rank one, J. Functional Analysis, 34 (1979), 54-71.
5) T. Kawazoe, An analogue of Paley-Wiener theorem on rank 1 semi-simple Lie groups I, Tokyo J. Math., 2 (1979), 397-407.
6) T. Kawazoe, An analogue of Paley-Wiener theorem on rank 1 semi-simple Lie groups II, Tokyo J. Math., 2 (1979), 409-421.
7) D. Milicic, Asymptotic behaviour of matrix coefficients of the discrete series, Duke Math. J., 44 (1977), 59-88.
8) P. C. Trombi and V. S. Varadarajan, Asymptotic behaviour of eigenfunctions on a semi-simple Lie group; The discrete spectrum, Acta Math., 129 (1972), 237-280.
9) P. C. Trombi and V. S. Varadarajan, Spherical transforms on semi-simple Lie groups, Ann. of Math., 94 (1971), 246-363.
10) G. Warner, Harmonic analysis on semi-simple Lie groups II, Springer-Verlag, Berlin, Heidelberg, New York, 1972.
11) V. S. Varadarajan, Harmonic analysis on real reductive groups, Lecture Notes in Math., 576, Springer-Verlag, 1977.
12) R. A. Kunze and E. M. Stein, Uniformly bounded representations and harmonic analysis on the 2×2 real unimodular group, Amer. J. Math., 82 (1960), 1-62.
13) R. Lipsman, Harmonic analysis on SL(n, C), J. Functional Analysis, 3 (1969), 126-155.
14) R. J. Stanton and P. A. Tomas, A note on the Kunze-Stein phenomenon, J. Functional Analysis, 29 (1978), 151-159.
15) M. Eguchi and K. Kumahara, Riemann-Lebesgue lemma for real reductive groups, Proc. Japan Acad. Ser. A Math. Sci., 56 (10) (1980), 465-468.

Right : [1] Harish-Chandra, Harmonic analysis on real reductive groups I, J. Functional Analysis, 19 (1975), 104-204.
[2] Harish-Chandra, Harmonic analysis on real reductive groups II, Invent. Math., 36 (1976), 1-55.
[3] Harish-Chandra, Harmonic analysis on real reductive groups III, Ann. of Math., 104 (1976), 117-201.
[4] K. D. Johnson, Paley-Wiener theorems on groups of split rank one, J. Functional Analysis, 34 (1979), 54-71.
[5] T. Kawazoe, An analogue of Paley-Wiener theorem on rank 1 semi-simple Lie groups I, Tokyo J. Math., 2 (1979), 397-407.
[6] T. Kawazoe, An analogue of Paley-Wiener theorem on rank 1 semi-simple Lie groups II, Tokyo J. Math., 2 (1979), 409-421.
[7] D. Milicic, Asymptotic behaviour of matrix coefficients of the discrete series, Duke Math. J., 44 (1977), 59-88.
[8] P. C. Trombi and V. S. Varadarajan, Asymptotic behaviour of eigenfunctions on a semi-simple Lie group; The discrete spectrum, Acta Math., 129 (1972), 237-280.
[9] P. C. Trombi and V. S. Varadarajan, Spherical transforms on semi-simple Lie groups, Ann. of Math., 94 (1971), 246-363.
[10] G. Warner, Harmonic analysis on semi-simple Lie groups II, Springer-Verlag, Berlin, Heidelberg, New York, 1972.
[11] V. S. Varadarajan, Harmonic analysis on real reductive groups, Lecture Notes in Math., 576, Springer-Verlag, 1977.
[12] R. A. Kunze and E. M. Stein, Uniformly bounded representations and harmonic analysis on the 2×2 real unimodular group, Amer. J. Math., 82 (1960), 1-62.
[13] R. Lipsman, Harmonic analysis on SL(n, C), J. Functional Analysis, 3 (1969), 126-155.
[14] R. J. Stanton and P. A. Tomas, A note on the Kunze-Stein phenomenon, J. Functional Analysis, 29 (1978), 151-159.
[15] M. Eguchi and K. Kumahara, Riemann-Lebesgue lemma for real reductive groups, Proc. Japan Acad. Ser. A Math. Sci., 56 (10) (1980), 465-468.

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